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→Description
<math>U_{ij} = \delta_{i+1,j}, \quad L_{ij} = \delta_{i,j+1}</math>.
<math>U_{ij} = \delta_{i+1,j}, \quad L_{ij} = \delta_{i,j+1}</math>.
where <math>\delta_{ij}</math> is the Kronecker delta symbol.
where <math>\delta_{ij}</math> is the Kronecker delta symbol.
*For example, the 5×5 shift matrices are:
*For example, the 5×5 shift matrices are
<math>U_5=\begin{pmatrix}
<math>U_5=\begin{pmatrix}
0 & 1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
\end{pmatrix}</math>
\end{pmatrix}</math>
*All shift matrices are nilpotent; an n by n shift matrix S becomes the null matrix when raised to the power of its dimension n.
*All shift matrices are nilpotent; an n by n shift matrix S becomes the null matrix when raised to the power of its dimension n.
==Examples==
*1.MATRIX("shift")
{| class="wikitable"
|-
| 0 || 1 || 0
|-
| 0 || 0 || 1
|-
| 0 || 0 || 0
|}
*2.MATRIX("shift",7)
{| class="wikitable"
|-
| 0 || 1 || 0 || 0 || 0 || 0 || 0
|-
| 0 || 0 || 1 || 0 || 0 || 0 || 0
|-
| 0 || 0 || 0 || 1 || 0 || 0 || 0
|-
| 0 || 0 || 0 || 0 || 1 || 0 || 0
|-
| 0 || 0 || 0 || 0 || 0 || 1 || 0
|-
| 0 || 0 || 0 || 0 || 0 || 0 || 1
|-
| 0 || 0 || 0 || 0 || 0 || 0 || 0
|}
==See Also==
*[[Manuals/calci/SIGNATURE| SIGNATURE]]
*[[Manuals/calci/CONFERENCE| CONFERENCE]]
*[[Manuals/calci/TRIANGULAR| TRIANGULAR]]
==References==